Yes, it's possible, but not easy. I did similar thing last year(left the previous program with M.S. in the end of 2nd year and applied to another Ph.D. program).
0 . Can I leave my current department with master degree in 2nd year?
It depends on your department policy and you should look at those policies carefully. No one on the internet can answer this question accurately.
Issues to consider in your new applications:
- Do you plan on changing department?
If you plan on going to a different department (not just different university, i.e. from university of X department of A to university of Y department of B where X\neq Y and A\neq B), you should explain, in your SOP, why do you have the ability to do well in the new field given your experience and knowledge background. If not, you should explain why similar department in a different university will be a better fit for you, in terms of research interest and general academic environment.
In any case, avoid saying "I hate the department I was previously in." or equivalent, that will make your applications look bad.
- What's your relation with current advisor and other faculties(in the department you're in now)? Who will be your recommender?
Ideally, if your current advisor support you and your decision, you should obtain letters from your current advisor. That will make things a lot easier. If, unfortunately, one of the reasons you're leaving is having personal confrontation with current advisor, you had better look for someone else. Spend some time figuring out who will write you a good letter that fits your new application well. Avoid people who may write bad letters as personal revenge.
Be aware that you'll be strictly barred from applying to some programs if you don't have at least one letter from the last university you attended. That's a issue to consider if you plan on having people from your undergraduate institution be your recommender.
- Do you need to retake exams like GRE?
GRE scores(subject or general) do not expire in 5 years. However some graduate programs may require a much more recent one(for example within 2 years). If you want to apply to those programs, you'll have to retake the GRE. If the new program require a subject GRE you've not taken before, you'll have to take it.